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Estimate of aliasing error for non-smooth signals prefiltered by quasi-projections into shift-invariant spaces

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3 Author(s)
Wen Chen ; Dept. of Electr. & Comput. Eng., Univ. of Alberta, Edmonton, Alta., Canada ; Bin Han ; Rong-Qing Jia

An ideal analog-to-digital (A/D) converter prefilters a signal by an ideal lowpass filter. Recent research on A/D conversion based on shift-invariant spaces reveals that prefiltering signals by quasiprojections into shift-invariant spaces provides more flexible choices in designing an A/D conversion system of high accuracy. This paper focuses on the accuracy of such prefiltering, in which the aliasing error efλ is found to behave like efλ 2 = O(λ) with respect to the dilation λ of the underlying shift-invariant space, provided that the input signal f is Lipschitz-α continuous. A formula to calculate the coefficient of the decay rate is also figured out in this paper.

Published in:

IEEE Transactions on Signal Processing  (Volume:53 ,  Issue: 5 )